We have developed a new experimental setup specifically designed for measuring thermal conductivity on technical superconductors in the range of temperatures 3-330 K in magnetic fields up to 21 T. Three Nb3Sn wires, produced by the powder-in-tube technique, the bronze route, and the internal tin restacked-rod process, respectively, have been investigated. We show that, due to the complexity of the architecture of these wires, direct measurement of thermal conductivity is required for a correct estimation of thermal stability in superconducting magnets.